There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ arcsin(bx)e^{c{x}^{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{cx^{2}}arcsin(bx)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{cx^{2}}arcsin(bx)\right)}{dx}\\=&e^{cx^{2}}c*2xarcsin(bx) + e^{cx^{2}}(\frac{(b)}{((1 - (bx)^{2})^{\frac{1}{2}})})\\=&2cxe^{cx^{2}}arcsin(bx) + \frac{be^{cx^{2}}}{(-b^{2}x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2cxe^{cx^{2}}arcsin(bx) + \frac{be^{cx^{2}}}{(-b^{2}x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&2ce^{cx^{2}}arcsin(bx) + 2cxe^{cx^{2}}c*2xarcsin(bx) + 2cxe^{cx^{2}}(\frac{(b)}{((1 - (bx)^{2})^{\frac{1}{2}})}) + (\frac{\frac{-1}{2}(-b^{2}*2x + 0)}{(-b^{2}x^{2} + 1)^{\frac{3}{2}}})be^{cx^{2}} + \frac{be^{cx^{2}}c*2x}{(-b^{2}x^{2} + 1)^{\frac{1}{2}}}\\=&2ce^{cx^{2}}arcsin(bx) + 4c^{2}x^{2}e^{cx^{2}}arcsin(bx) + \frac{2bcxe^{cx^{2}}}{(-b^{2}x^{2} + 1)^{\frac{1}{2}}} + \frac{b^{3}xe^{cx^{2}}}{(-b^{2}x^{2} + 1)^{\frac{3}{2}}} + \frac{2bcxe^{cx^{2}}}{(-b^{2}x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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